Asymptotic properties of maximum likelihood estimators in models with multiple change points

TL;DR

This paper investigates the asymptotic behavior of maximum likelihood estimators in models with multiple change points, establishing their consistency, convergence rates, and asymptotic distributions for a broad class of models.

Contribution

It provides the first comprehensive theoretical analysis of MLE properties in multiple change-point models, including consistency and distributional results.

Findings

MLE of change points are consistent

Convergence rates of MLE are established

Asymptotic distributions of parameter estimators are derived

Abstract

Models with multiple change points are used in many fields; however, the theoretical properties of maximum likelihood estimators of such models have received relatively little attention. The goal of this paper is to establish the asymptotic properties of maximum likelihood estimators of the parameters of a multiple change-point model for a general class of models in which the form of the distribution can change from segment to segment and in which, possibly, there are parameters that are common to all segments. Consistency of the maximum likelihood estimators of the change points is established and the rate of convergence is determined; the asymptotic distribution of the maximum likelihood estimators of the parameters of the within-segment distributions is also derived. Since the approach used in single change-point models is not easily extended to multiple change-point models, these results require the introduction of those tools for analyzing the likelihood function in a multiple change-point model.